(x-5)(x-7)=-13x+47

Solution for (x-5)(x-7)=-13x+47 equation:

(x-5)(x-7)=-13x+47

We move all terms to the left:

(x-5)(x-7)-(-13x+47)=0

We get rid of parentheses

(x-5)(x-7)+13x-47=0

We multiply parentheses ..

(+x^2-7x-5x+35)+13x-47=0

We get rid of parentheses

x^2-7x-5x+13x+35-47=0

We add all the numbers together, and all the variables

x^2+x-12=0

a = 1; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·1·(-12)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*1}=\frac{6}{2}
=3
$